SWH again (was Re: What's going on here?)

[Edward Cherlin <cherlin@CAUCE.ORG>]

At 1:16 PM -0700 10/25/97, Chris Bogart wrote:
>On Sun, 26 Oct 1997, HACKER G N wrote:
[snip]

>> But in terms of actually making the distinction at all, you don't need a
>> language to do that, you just make the distinction. What a language can do
>> is find a convenient way of expressing that distinction to others.
>
>For me at least, though, it could help me think about the matter more
>smoothly, and therefore more quickly or more often, at least within a
>certain category of thinking.
>
>This is all very theoretical -- I have no idea how I could ever prove this
>to myself for sure, much less anyone else.  But I suppose that's an
>inherent problem when discussing something as immeasurable as "thought".

A practical example is Conway's recent recasting of the theory of games in
terms of extended non-standard arithmetic. A number is defined as an
ordered pair of sets of numbers, where each member of the Left set is less
than each member of the Right set. A game is an ordered pair of sets of
games, without restriction. Both constructions begin with the number 0 = {
|  } in which both Left and Right sets are empty. Then { 0 |  } is a number
(1), { 0 | 1 } is a number (1/2), and { 0 | 0 } is a game (*). This game *
is infinitesimal, and neither greater than 0, less than 0, or equal to 0.

Using this theory, Elwyn Berlekamp, a middle-level amateur, is able to
create Go positions in which he can routinely beat the top players in the
world with either color. He thinks in the new language (up, star, tiny,
miny...), they think in the traditional language of Go (sente, gote...) and
he wins, over and over.

The concepts cannot be explained in the old terminology, and the
distinctions cannot be made without the new terminology. You can think of
making one distinction at a time without new language, but not the hundreds
required to use the new theory of Go endgames. See "Mathematical Go
Endgames: Nightmares for Professional Go Players" by Berlekamp and Wolfe,
for details. ISBN  0-923891-36-6. There is also a hardcover edition under
the title, "Mathematical Go: Chilling Gets the Last Point".

Other practical cases of great interest are recounted by Oliver Sachs in
"The Man Who Mistook His Wife for a Hat." The most interesting for this
discussion is the artist with achromatopsia. Due to neurological damage, he
lost not only the ability to see colors, but all memory of what colors
looked like. He could still describe colors by name and by Pantone matching
number. It turned out, however, that his knowledge of color went no further
than names and numbers. All the rest of his understanding of color was
lost.

The point is that language by itself does not provide the means for
thought. Language and other mental abilities have to work together so that
the language refers to something--a memory, a mental model, or whatever,
which we hope is connected to reality--and the user can work in the
language or the concepts or both, whichever is more appropriate at the
moment.

--
Edward Cherlin, President      <http://www.cauce.org/>
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